Advances in Combinatorial Methods and Applications to Probability and Statistics

1. Front Matter

   Pages i-xxxiv

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2. Lattice Paths and Combinatorial Methods

   1. Front Matter

      Pages 1-1

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   2. Lattice Paths and Faber Polynomials

      • Ira M. Gessel, Sangwook Ree

      Pages 3-13

   3. Lattice Path Enumeration and Umbral Calculus

      • Heinrich Niederhausen

      Pages 15-27

   4. The Enumeration of Lattice Paths With Respect to Their Number of Turns

      • C. Krattenthaler

      Pages 29-58

   5. Lattice Path Counting, Simple Random Walk Statistics, and Randomization: An Analytic Approach

      • Wolfgang Panny, Walter Katzenbeisser

      Pages 59-76

   6. Combinatorial Identities: A Generalization of Dougall’s Identity

      • Erik Sparre Andersen, Mogens Esrom Larsen

      Pages 77-88

   7. A Comparison Of Two Methods For Random Labelling of Balls by Vectors of Integers

      • Doron Zeilberger

      Pages 89-93

3. Applications to Probability Problems

   1. Front Matter

      Pages 95-95

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   2. On The Ballot Theorems

      • Lajos Takàcs

      Pages 97-114

   3. Some Results for Two-Dimensional Random Walk

      • Endre Csáki

      Pages 115-124

   4. Random Walks on SL(2, F2) and Jacobi Symbols of Quadratic Residues

      • Toshihiro Watanabe

      Pages 125-134

   5. Rank Order Statistics Related to a Generalized Random Walk

      • Jagdish Saran, Sarita Rani

      Pages 135-151

   6. On a Subset Sum Algorithm and Its Probabilistic and Other Applications

      • V. G. Voinov, M. S. Nikulin

      Pages 153-163

   7. I and J Polynomials in a Potpourri of Probability Problems

      • Milton Sobel

      Pages 165-187

   8. Stirling Numbers and Records

      • N. Balakrishnan, V. B. Nevzorov

      Pages 189-200

4. Applications to Urn Models

   1. Front Matter

      Pages 201-201

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   2. Advances in Urn Models during the Past Two Decades

      • Samuel Kotz, N. Balakrishnan

      Pages 203-257

   3. A Unified Derivation of Occupancy and Sequential Occupancy Distributions

      • A. Charalambides

      Pages 259-273

   4. Moments, Binomial Moments and Combinatorics

      • Janos Galambos

      Pages 275-284

Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer­ sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.

• Binomial distribution
• Counting
• Derivation
• Finite
• Identity
• Random variable
• STATISTICA
• Variable
• algorithms
• equation
• probability
• proof
• standard deviation
• statistics
• theorem

• Department of Mathematics, McMaster University, Hamilton, Canada

  N. Balakrishnan

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